This paper is a sequel to an evolving research project on a diagrammatic methodology called thinging machine (TM). Initially, it was proposed as a base for conceptual modelling (e.g., conceptual UML) in areas such as requirement engineering. Conceptual modelling involves a high-level representation of a real-world system that integrates various components to refine it into a more concrete (computer) executable form. The TM project has progressed into a more comprehensive approach by applying it in several research areas and expanding its theoretical and ontological foundation. Accordingly, the first part of the paper involves enhancing some TM aspects related to structuring events in existence, such as absent events. The second part of the paper focuses on how to classify events and the kinds of relationships that can be recognized among events. The notion of events has occupied a central role in modelling. It influences computer science and such diverse disciplines as linguistics, probability theory, artificial intelligence, physics, philosophy and history. In TM, an event is defined as the so-called thimac (thing/machine) with a time breath that infuses dynamism into the static description of the thimac called a region. A region is a diagrammatic specification based on five generic actions: create, process, release, transfer and receive. The results of this research provide (a) an enrichment of conceptual modelling, especially concerning varieties of existence, e.g., absent events of negative propositions, and (b) a proposal that instead of semantic categorizations of events, it is possible to develop a new type of classification based on graphs grounded on the TM model diagrams.